Related papers: Gaussian distributions on Riemannian symmetric spa…
We provide a general framework for constructing probability distributions on Riemannian manifolds, taking advantage of area-preserving maps and isometries. Control over distributions' properties, such as parameters, symmetry and modality…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
Distribution learning focuses on learning the probability density function from a set of data samples. In contrast, clustering aims to group similar objects together in an unsupervised manner. Usually, these two tasks are considered…
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…
Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. This paper pursues three main…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning. Consequently, understanding the Riemannian geometry of SPD matrices has attracted much attention lately. A particular Riemannian geometry of…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges…
The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…